Design and analysis of gradient-based differential neural network for solving time-varying quadratic problems with
Yang Zeng1, Cheng Hua2, Bolin Liao2
1College of Computer Science and Engineering, Jishou University, Jishou, 416000, Hunan, China; College of Communication and Electronic Engineering, Jishou University, Jishou, 416000, Hunan, China.
Summary
A novel gradient-differential neural network (GDNN) efficiently solves inequality-constrained time-varying quadratic programs (IC-TVQP). This advanced model demonstrates superior accuracy and robustness compared to existing methods.
Area of Science:
- Optimization
- Computational Science
- Artificial Intelligence
Background:
- Inequality-constrained time-varying quadratic programs (IC-TVQP) present significant computational challenges.
- Existing methods often lack efficiency and accuracy for dynamic, constrained optimization problems.
Purpose of the Study:
- Introduce a novel gradient-differential neural network (GDNN) for effective IC-TVQP resolution.
- Enhance computational efficiency and ensure finite-time convergence for IC-TVQP.
Main Methods:
- Developed a GDNN incorporating a refined sign-bi-power activation function.
- Conducted comparative analyses against conventional gradient-based neural networks (CGNN), varying-parameter convergence differential neural networks (VP-CDNN), and zeroing neural networks (ZNN).
- Performed extensive numerical simulations to validate performance and robustness.
Main Results:
- The GDNN achieved superior solution accuracy with significantly lower residual errors compared to CGNN, VP-CDNN, and ZNN.
- Demonstrated enhanced robustness to variations in scaling factors.
- Successfully applied the GDNN to a time-varying financial portfolio optimization problem.
Conclusions:
- The proposed GDNN offers a highly effective and efficient solution for IC-TVQP.
- The model exhibits practical applicability and robustness in real-world optimization scenarios.
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